What does progress look like?

Recently I was at university for a day of lectures towards my MA. During one of the sessions the professor posed the question: “what does progress look like in your subject?” and this really started me thinking about progress, and perceived progress.

Mostly, when folk talk about progress they are talking in quantitative terms. They are talking about progress from one level to the next via performance on a predetermined exam. This is an idea that worries me.

Last summer, edexcel threw us a curveball with a c3 paper that (shock horror) not only failed to ask the same questions in the same order, but that tested some assumed prior knowledge (i.e. That speed = distance /time and that sin a = cos (90-a) ). (You can read Colin Beveridge aka @icecolbeveridge ‘s post on the exam here .)This threw up a rather interesting result in my year 13 class. Pupil a who normally scored the highest scored lowest on this test, scoring lower than his others, where as pupil b who normally scored lowest scored the highest and his marks were not as significantly affected as the rest. The most remarkable thing was that this was exactly as I expected. Pupil A was top through solid hard work, he wasn’t as naturally mathematical as the rest, but put his all in all the time. Pupil b was by far and away the most naturally gifted mathematician in the class, but didn’t work anything like as hard. If I look at the paper results, over the course of the a level pupil a had made more progress (not a full grades worth, but quite a few UMS points), but I feel pupil b has a much better mathematical understanding and is much better placed to study maths further at university. Surely then, pupil b has made more progress?

This isn’t limited towards a level, across the board examining bodies have consistently set paper after paper using the same formulaic questions, which has encouraged a culture of teaching to the exam. This isn’t the way it should be. I (and many others I might add) believe that we should teach for understanding, rather than teaching “this question means type… Into your calculator.”

I would favour a world where exams where unpredictably diverse in their questions. Where they examined a deeper understanding of the subject. I feel this is what is needed to improve the quality of our future mathematicians, and those who go on to study other areas! (Dave Gale, aka @reflectivemaths, has this to say on the future of maths exams, and I’ve written on the topic previously here)

In short: what does progress in maths look like? A greater mathematical understanding, and as such, a greater ability to make sense of the world.

You’re quite right that this isn’t just a problem at A-level – at university, too (at least, 15 years ago), you could confidently predict the question types that would come up in the exam and get good grades based on almost rote learning.

The big question for me is, what is maths A-level FOR? Is it to teach techniques – which is what it’s been doing at least since I started teaching – or to teach mathematical thinking, which is what I’d prefer? The C3 paper was a step in that direction (the questions weren’t formulaic, although I think Kate the photographer was framed) – however, it did come a bit out of the blue.

I’m going to guess that Student B never once said “I’d never have thought of that”, while Student A did.

Now that you mention university, there is definitely some bells ringing. There was one young lady on y degree course who left with a fist, but had very little mathematical understanding, she had just learned methods to answer types of questions.

I’m very much in agreement that the c3 paper was a step in the right direction, but I also agree that it will have hurt many pupils grades, probably unfairly, to change the goalpost without warning.